Question: Solve for $x$ and $y$ using elimination. ${-3x-3y = -27}$ ${3x-2y = 12}$
We can eliminate $x$ by adding the equations together when the $x$ coefficients have opposite signs. Add the equations together. Notice that the terms $-3x$ and $3x$ cancel out. $-5y = -15$ $\dfrac{-5y}{{-5}} = \dfrac{-15}{{-5}}$ ${y = 3}$ Now that you know ${y = 3}$ , plug it back into $\thinspace {-3x-3y = -27}\thinspace$ to find $x$ ${-3x - 3}{(3)}{= -27}$ $-3x-9 = -27$ $-3x-9{+9} = -27{+9}$ $-3x = -18$ $\dfrac{-3x}{{-3}} = \dfrac{-18}{{-3}}$ ${x = 6}$ You can also plug ${y = 3}$ into $\thinspace {3x-2y = 12}\thinspace$ and get the same answer for $x$ : ${3x - 2}{(3)}{= 12}$ ${x = 6}$